Old English grighund, from grig- "bitch" + hund "dog" (see hound (n.)). The name usually is said to have nothing to do with color, and most are not gray. The Old Norse form of the word is preserved in Hjalti's couplet that almost sparked war between pagans and Christians in early Iceland:

(Prov. 30:31), the rendering of the Hebrew _zarzir mothnayim_, meaning literally "girded as to the lions." Some (Gesen.; R.V. marg.) render it "war-horse." The LXX. and Vulgate versions render it "cock." It has been by some interpreters rendered also "stag" and "warrior," as being girded about or panoplied, and "wrestler." The greyhound, however, was evidently known in ancient times, as appears from Egyptian monuments.